A small town has two service stations, which share the town’s market for gasoline. The owner of Station A is debating whether to give away free glasses to her customers as part of a promotional scheme, and the owner of Station B is debating whether to give away free steak knives. They know (from similar situations elsewhere) that if Station A gives away free glasses and Station B does not give away free steak knives, Station A’s share of the market will increase by 6 percent; if Station B gives away free steak knives and Station A does not give away free glasses, Station B’s share of the market will increase by 8 percent; and if both stations give away the respective items, Station B’s share of the market will increase by 3 percent.
(a) Present this information in the form of a payoff table in which the entries are Station A’s losses in its share of the market.
(b) Find optimum strategies for the owners of the two stations.